If you are convinced that your nitrite is over 16 ppm after a diluted test- then you do need to do a water change. You do not have to get anywhere near all the nitrite out.Iif you reduce it towards 10 ppm on the API diluted test, you are fine.
However, bear this in mind. The most nitrite that 1 ppm of ammonia can possibly make is 2.55 ppm. If all you did was to add 3 ppm twice and then 1 ppm your total is 7 ppm. That means your nitrite should not be above 7 x 2.55 = 17.85 ppm. However, for the nitrite to get to the max level is not likely since, as soon as nitrite shows up from the first ammonia dose, the nitrite bacs start to multiply and continue doing so unless your nitrite gets too high. So they will have processed some of that nitrite along the way. For partial conversion in the case of adding a total 7 ppm of ammonia it only needs about 3 ppm of that potential total to be reduced to nitrate to get the reading under 16 ppm.
So if you did the dosing according to how it is laid out in the article, it is almost impossible to get nitrite at cycle stalling levels. The entire dosing regimen in that article is designed to make it impossible to get nitrite too high as long as the directions are followed to the letter. And, in your case doing a water change, which is not suggested unless things go wrong, would have worked to remove ammonia and nitrite as a side effect. So, if you have indeed only dosed 7 ppm of ammonia and then you have done a water change, your test readings cannot be correct. If you changed just 20% of the water with nitrite at 17.85, the result would have been a reading of nitrite at 14.28 ppm. And if you changed more, then that number should have been even lower.
At a 50% dilution a 5 ppm nitrite reading indicates a level of 10 ppm or more, at 75% dilution it means 20 ppm or more. Note, I did not use the terms 2-1 or 4-1 but rather the %s of each water source. 2:1 or 4:1 are ratios, they would imply 2/3 and 1/3 or 4/5 and 1/5. At 75% dilution 1/4 of the reading is real since 1/4 of the water is from the tank. That is why the factor is to multiply by 4. In the normal test, without dilution, the factor would be 1 x the result. Doing the math in reverse makes this clearer. If you had 20 ppm. 1/4 of this is 5 ppm. The danger of using the 2:1 or 4:1 designation is, if used, it does not mean the same thing.
For those out there who are nudges about this sort of thing- the 50% test has a 1:1 ratio of tank to distilled while the 75% dilution has a ratio of 3:1.